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Vl-make-list-of-bitselects

Build a list of expressions, (expr[low] ... expr[high]).

Signature

(vl-make-list-of-bitselects expr low high) → exprs

Arguments

expr — Guard (vl-expr-p expr).

low — Guard (natp low).

high — Guard (natp high).

Returns

exprs — Type (vl-exprlist-p exprs).

Definitions and Theorems

Function: vl-make-list-of-bitselects

(defun vl-make-list-of-bitselects (expr low high)
  (declare (xargs :guard (and (vl-expr-p expr)
                              (natp low)
                              (natp high))))
  (declare (xargs :guard (<= low high)))
  (let ((__function__ 'vl-make-list-of-bitselects))
    (declare (ignorable __function__))
    (if (mbe :logic (zp (- (nfix high) (nfix low)))
             :exec (eql high low))
        (list (vl-make-bitselect expr low))
      (cons (vl-make-bitselect expr low)
            (vl-make-list-of-bitselects expr (+ (nfix low) 1)
                                        high)))))

Theorem: vl-exprlist-p-of-vl-make-list-of-bitselects

(defthm vl-exprlist-p-of-vl-make-list-of-bitselects
  (b* ((exprs (vl-make-list-of-bitselects expr low high)))
    (vl-exprlist-p exprs))
  :rule-classes :rewrite)

Theorem: len-of-vl-make-list-of-bitselects

(defthm len-of-vl-make-list-of-bitselects
  (equal (len (vl-make-list-of-bitselects expr low high))
         (+ 1 (nfix (- (nfix high) (nfix low))))))

Theorem: vl-exprlist->finalwidths-of-vl-make-list-of-bitselects

(defthm vl-exprlist->finalwidths-of-vl-make-list-of-bitselects
  (equal (vl-exprlist->finalwidths
              (vl-make-list-of-bitselects expr low high))
         (replicate (+ 1 (nfix (- (nfix high) (nfix low))))
                    1)))

Theorem: vl-exprlist->finaltypes-of-vl-make-list-of-bitselects

(defthm vl-exprlist->finaltypes-of-vl-make-list-of-bitselects
  (equal (vl-exprlist->finaltypes
              (vl-make-list-of-bitselects expr low high))
         (replicate (+ 1 (nfix (- (nfix high) (nfix low))))
                    :vl-unsigned)))

Theorem: vl-make-list-of-bitselects-of-vl-expr-fix-expr

(defthm vl-make-list-of-bitselects-of-vl-expr-fix-expr
  (equal (vl-make-list-of-bitselects (vl-expr-fix expr)
                                     low high)
         (vl-make-list-of-bitselects expr low high)))

Theorem: vl-make-list-of-bitselects-vl-expr-equiv-congruence-on-expr

(defthm vl-make-list-of-bitselects-vl-expr-equiv-congruence-on-expr
  (implies (vl-expr-equiv expr expr-equiv)
           (equal (vl-make-list-of-bitselects expr low high)
                  (vl-make-list-of-bitselects expr-equiv low high)))
  :rule-classes :congruence)

Theorem: vl-make-list-of-bitselects-of-nfix-low

(defthm vl-make-list-of-bitselects-of-nfix-low
  (equal (vl-make-list-of-bitselects expr (nfix low)
                                     high)
         (vl-make-list-of-bitselects expr low high)))

Theorem: vl-make-list-of-bitselects-nat-equiv-congruence-on-low

(defthm vl-make-list-of-bitselects-nat-equiv-congruence-on-low
  (implies (acl2::nat-equiv low low-equiv)
           (equal (vl-make-list-of-bitselects expr low high)
                  (vl-make-list-of-bitselects expr low-equiv high)))
  :rule-classes :congruence)

Theorem: vl-make-list-of-bitselects-of-nfix-high

(defthm vl-make-list-of-bitselects-of-nfix-high
  (equal (vl-make-list-of-bitselects expr low (nfix high))
         (vl-make-list-of-bitselects expr low high)))

Theorem: vl-make-list-of-bitselects-nat-equiv-congruence-on-high

(defthm vl-make-list-of-bitselects-nat-equiv-congruence-on-high
  (implies (acl2::nat-equiv high high-equiv)
           (equal (vl-make-list-of-bitselects expr low high)
                  (vl-make-list-of-bitselects expr low high-equiv)))
  :rule-classes :congruence)